As a young mathematician in the 1950s, the late Don Newman taught at the Massachusetts Institute of Technology alongside rising star and Nobel-laureate-to-be John Nash. Newman had been struggling to solve a particular math problem: “I was ... trying to get somewhere with it, and I couldn't and I couldn't and I couldn't,” he recalled.

One night Newman dreamed that he was reflecting on the problem when Nash appeared. The sleeping Newman related the details of the conundrum to Nash and asked if he knew the solution. Nash explained how to solve it. Newman awoke realizing he had the answer! He spent the next several weeks turning the insight into a formal paper, which was then published in a mathematics journal.

Newman is hardly alone in making a practical breakthrough during a night of sleep. While dreaming, Friedrich August Kekulé came up with the structure of benzene, Dmitry Mendeleev conjured up his final form of the periodic table of the elements and Otto Loewi thought of the neuroscience experiment that won him a Nobel Prize in medicine.

Modern engineers Paul Horowitz and Alan Huang dreamed designs for laser-telescope controls and laser computing, respectively. Innumerable artists and filmmakers have depicted images that came to them in their sleep. Mary Shelley dreamed the two main scenes that became Frankenstein, and Robert Louis Stevenson did the same with Dr. Jekyll and Mr. Hyde. Ludwig van Beethoven, Paul McCartney and Billy Joel all awoke to discover new tunes ringing in their minds. Mahatma Gandhi's call for a nonviolent protest of British rule of India was inspired by a dream.

Yet dreams so often seem incoherent, bizarre or even trivial. We search intensely for our brother in an endless maze of corridors because we must give him a yellow package. But when we find him, we have forgotten the package—which we are certainly not holding any longer—and anyway he is now a neighbor, not a brother. Other dreams are ephemeral—we wake up thinking about a yellow box, but that is all we recall.

For decades scientists have puzzled over how dreams could display such diverse characteristics. Research is beginning to suggest that dreams are simply thought in a different biochemical state. The physiological demands of sleep alter the way the brain functions. Dreams may seem bizarre or nonsensical because the chemistry of the sleeping brain affects how we perceive our own thoughts, but we nonetheless continue focusing on all the same issues that concern us while we are awake. This unusual state of consciousness is often a blessing for problem solving—it helps us find solutions outside our normal patterns of thought. By following a few simple steps, we can even harness this power, encouraging our sleeping brain to ruminate on particular concerns.

Anatomy of a Dream

One often hears the question, “What is dreaming for?” You would never pose such a simplistic query about waking thought. It is for everything.

Nevertheless, theorists have long offered one-function explanations for dreaming. Sigmund Freud believed that dreams primarily express repressed wishes, namely infantile sexual and aggressive impulses. Other psychoanalysts thought dreams had more to do with narcissistic strivings or compensation for feelings of inferiority. More recently, psychologists have posited that dreams simulate threats or help to consolidate memories. All these theories characterize some dreams, but none of them can account for every type. Just as waking thought can drift between reminiscing, planning, rumination, and so on, dream cognition seems to encompass many modes of thought.

Most early theorists assumed that the dreams we remembered constituted all dreams. Several hypotheses supposed that people experienced dreams when some specific situation triggered a set of distinctive feelings—the desire for sex, say, or a bruised ego. In the 1950s, however, a series of groundbreaking studies by Eugene Aserinsky and Nathaniel Klietman, both then at the University of Chicago, revealed that people have many more dreams than they are likely to remember. The two sleep researchers discovered that human slumber consists of approximately 90-minute cycles, each one containing a period of rapid eye movement (REM) and heightened brain activity—about as much activity as when we are awake. When the scientists awakened people near the end of each REM period, the sleepers recounted an average of almost five dreams per night. The discrepancy between the subjects' reports when awakened right after the REM period, as opposed to later, led the scientists to conclude that dreams almost always accompany this stage of sleep even if none are recalled by the morning.

Within the past two decades positron-emission tomography (PET) scans have allowed us to see which brain areas are involved in dreaming. Parts of the cortex associated with visual imagery and the perception of movement become activated even more dramatically than when we are awake, as do some deep brain areas associated with emotion. In contrast, the dorsolateral prefrontal cortex is less engaged during dreaming; this area is associated with volitional action and the evaluation of what is logical and socially appropriate. These PET results fit the characteristics of dreams well; dream reports almost always contain visual imagery and often involve movement. The prefrontal findings fit neatly with the fact that dreams have long been associated with less “censorship”—not only in the Freudian sense of uninhibited sex and aggression but also in terms of our filtering out scenarios that are illogical or abnormal. We will return to this point when discussing methods of problem solving. Sometimes tackling a puzzle the “wrong” way can lead to surprising insights.

Evolutionary psychologists were quick to point out that this PET portrait of the dreaming brain makes sense because such activity would have supported human survival—certain areas of the brain are safer to turn on and off during sleep than others. Donald Symons, an anthropologist at the University of California, Santa Barbara, argued in his 1993 paper “The Stuff That Dreams Aren't Made Of” that sleepers must monitor the environment with specific senses—to smell smoke, hear intruders, sense temperature changes and feel pain. Hallucinating vividly in those sensory modes might lead us to wake up frequently in an unnecessary panic, or, even worse, over a long period we might evolve a threshold of tolerance that would cause us to block our real warnings. Our eyes can be closed, however, because we do not need to monitor our visual environment during sleep. And our body can be paralyzed, as is normal during REM sleep, because we do not need to move—in fact, we should not move until we awaken.

Evolution, then, may help elucidate why certain brain areas are more or less active when we sleep. The pattern of activity explains why dreams have the characteristics they do—visually rich and logically loose. At first, these exciting physiological findings gave rise to a proliferation of theories that dreams were just an epiphenomenon, or side effect, of the brain patterns during slumber. Sleep researchers often referred to REM activity as “random,” although no evidence suggested it was any more random than waking brain activity. Many theorists leaped to pronounce dreams “explained.”

I reiterate: we would never dismiss waking thought so quickly. Knowing that our prefrontal cortex is active when we encounter a social prohibition does not explain away the subjective debate we experience when deciding how to respond. Likewise, describing a dream's content or its associated brain activity does not answer the question of its purpose. Brain researchers finally grasped this fact after a two-decade lull and in the past few years have begun studying dreams seriously again.

Sleep on It

By the 1990s a growing body of research suggested that slumber is important for consolidating new learning: even very early studies had shown that sleeping for a while after learning something new results in much better recall than after spending the same amount of time awake. More recent findings hint at a special role for REM sleep in memory consolidation. Studies of rats learning to navigate mazes have found that during REM sleep, brain activity mimics that of the awake rodent training in the maze, which suggests that circuits may be reinforced during REM sleep. In humans, too, research supports the role of REM sleep in memory. The more REM sleep subjects get after learning, the better they recall emotionally charged material.

In 2009 psychologists at the University of California, San Diego, examined whether REM facilitated more than just memory when learning. They gave their subjects a test that required creative problem solving and then dropped hints about the answers. The subjects then spent some time either awake, in non-REM sleep only or in REM sleep before taking the test again. The REM sleep group showed the most improvement on their creative solutions to the previously presented problems.

The same year in Robert Stickgold's lab at Harvard University, a team led by postdoctoral researcher Ina Djonlagic had subjects learn a complicated system of weather prediction. The students were shown a combination of images, each representing a probability of sun or rain. The students did not know the meaning of the images, but they attempted to figure them out through trial and error by predicting an overall chance of sun or rain and getting feedback on their answers. The researchers found that subjects who nodded off before doing the task again were more likely to discover the general rule behind the images' meaning through an “aha!” type of insight than those who stayed awake. In addition, their heightened performance, as well as their ability to explicitly articulate that they had grasped the general rule, was correlated with the amount of REM sleep they had gotten.

Further research confirms that REM sleep aids in problem solving. In a series of ongoing studies in the same Harvard lab, postdoctoral researcher Erin J. Wamsley asks subjects to navigate a virtual maze. After some practice, they get either a waking break, REM sleep or a non-REM sleep period. As Wamsley reported at the 2011 SLEEP conference, only REM sleep sharpens participants' performance. In addition, when she wakes or interrupts them to ask what they are thinking or dreaming, the theme is often the maze—but only when this thinking occurs in REM sleep do subjects fare better the next time they tackle the real maze.

Because REM sleep is the stage during which dreams occur, these sleep studies imply that dreaming might have something to do with creative problem solving. Mounting experimental evidence, as well as countless anecdotes of solutions that popped up during dreams, supports this idea.

The first study on dreams and objective problem solving was conducted more than a century ago. In 1892 Charles M. Child of Wesleyan University asked 186 college students whether they had ever addressed a problem in a dream. One third said they had. The students reported playing a chess game, solving an algebra problem, detecting a bookkeeping error and translating a passage from Virgil while slumbering.

The next major breakthrough came when researchers decided to try seeding people's dreams with a specific problem. In 1972 sleep researcher William Dement of Stanford University asked 500 of his students to spend 15 minutes a night trying to solve brainteasers, making sure that they fell asleep with an unsolved problem on their mind. Students reported having 87 dreams, seven of which solved a brainteaser.

Such puzzles are a useful tool for testing creative problem solving because people are likely to get stuck before having an “aha!” moment of insight. Yet these brainteasers may be beyond the ability of some subjects, and they are also not of great personal import. In Dement's study, which lasted three nights, all the correct answers came during the first night. He surmised that students lost motivation quickly on problems of little relevance to their lives. Therefore, in my own research in 1996, I took a different approach. I asked students to select their own objective problem. They recorded their dreams for a week and noted the ones they thought addressed the issue or contained a satisfactory solution. Two research assistants also judged whether the dreams focused on or solved the problems.

Most of my subjects chose problems that appeared simpler than Dement's brainteasers. Half of them had dreams they felt touched on their concern, and one third dreamed a solution to it. Judges rated only slightly fewer dreams as tackling or solving problems. Although a number of the problems had to do with homework or mundane tasks such as rearranging furniture, some of the most interesting solutions came up in dreams about major life decisions. For instance, this dilemma was rated as solved by both the dreamer and the judges:

Problem: I have applied to two programs in clinical psychology and two in industrial psychology because I can't decide which field I want to go into.

Dream: There's a map of the U.S., and I'm in a plane flying over this map. The pilot says we're having engine trouble and need to land. We look for a safe place on the map, indicated by a light. I ask about Massachusetts, which we're right over, but he says that all of Massachusetts is very dangerous. The lights seemed to be farther west.

Solution: I woke up and realized that my two clinical schools are both in Massachusetts, where I have spent my entire life and where my parents live. Both industrial programs are far away, in Texas and California. This is because originally I was looking to stay close to home, and there were no good industrial programs nearby. I realized that there is a lot wrong with staying at home, and funny as it sounds, getting away is probably more important than which kind of program I go into.

A Portal to Creativity

The all-time most famous dream example—Kekulé realizing that the structure of benzene was a closed ring after dreaming of a snake made of atoms taking its tail in its mouth—illustrates the two distinctive features of problem solving in dreams. Recall that the brain areas that usually restrict our thinking to the logical and familiar are much less active during REM sleep. Many studies of creativity suggest that such disinhibition is a crucial component of creative thought. [For more on how cognitive disinhibition allows new ideas to surface, see “The Unleashed Mind,” by Shelley Carson, on page 28.] Similarly, the high activity in the visual areas of the sleeping brain allows it to visualize solutions more readily than in waking thought. Kekulé had been stumped because all known molecules were straight lines with side chains, and he had assumed, wrongly, that benzene would follow suit.

My research confirms that dreamed solutions tend to have unusual visual characteristics. Through the late 1990s I scoured the existing literature on dreams, combed professional biographies and history books for examples of problem-solving dreams, and queried working professionals as to whether they had ever had dreams that were useful in their jobs. Certain patterns emerged from this research. Well over half of the visual artists said they had used dreams in their work. About half of fiction writers had. The numbers dropped off rapidly as the professions became more abstract. Within the sciences, inventors, engineers and others who benefit from visualizing problems in three dimensions were likelier to report helpful dreams. Some dreamers even had multiple examples of having awakened with a solution and had developed an explicit bedtime incubation routine.

In a recent study, for which I reported preliminary results in June 2011 at the International Association for the Study of Dreams Conference, I investigated how dream-based problem solving might benefit working men and women more broadly. Professionals aged 21 to 69 attempted to solve real work-related problems in their sleep. These subjects seemed to dream about their problems with the same frequency as the college students I had observed in 1996; however, they reported less than half the number of solutions as compared with the students. The work-related problems may simply be more difficult than the college students' dilemmas, and because this group is older, the subjects may not recall as many dreams. A significant number of them, however, did report having a useful dream after only one week of incubation practice.

Your Dreams

Shortly after my book The Committee of Sleep was published in 2001, I heard Newman recount his story on a PBS show about John Nash and the film A Beautiful Mind. A year later I was unexpectedly seated next to Nash at a dinner party. I asked him about the incident, which he remembered well. “Don actually included a footnote thanking me in the paper,” Nash chuckled, “and he kept acting grateful, like I'd actually helped him when it was his dream.” I came across that remark often in my survey. Solutions frequently came from a dream character—one computer programmer got repeated nocturnal lessons from Albert Einstein—and people had trouble taking full credit for what their dreaming mind had done. This tendency fits brain findings for REM sleep in which the dorsolateral prefrontal cortex, associated with perceptions of volition, is less active than parts of the brain associated with perceptions of visual images, movement and emotions.

But we need not wait passively for inspiration to strike. We spend almost a third of our lives asleep—and almost a third of that time dreaming. My research suggests that in a short amount of time, people can learn to focus their dreams on minor problems and often solve them [see box on opposite page]. As for the bigger concerns, surveys find that all kinds of mysteries can be revealed in dreams—two Nobel Prizes resulted from dreams, after all. But even if you choose to leave your sleeping brain alone, pay attention: after nodding off, your brain in its altered state of consciousness is very likely already hard at work.